Vol. 12, No. 6, 2019

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Occurrence graphs of patterns in permutations

Bjarni Jens Kristinsson and Henning Ulfarsson

Vol. 12 (2019), No. 6, 901–918

We define the occurrence graph Gp(π) of a pattern p in a permutation π as the graph whose vertices are the occurrences of p in π, with edges between the vertices if the occurrences differ by exactly one element. We then study properties of these graphs. The main theorem in this paper is that every hereditary property of graphs gives rise to a permutation class.

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graph, permutation, subgraph, pattern
Mathematical Subject Classification 2010
Primary: 05A05, 05A15, 05C30
Received: 11 July 2016
Revised: 15 February 2019
Accepted: 18 February 2019
Published: 3 August 2019

Communicated by Anant Godbole
Bjarni Jens Kristinsson
Department of Mathematics
University of Iceland
Henning Ulfarsson
School of Computer Science
Reykjavik University